14edo: Difference between revisions

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14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

14edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].

14edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]] or 18:22:27.

=== Prime harmonics ===

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== Approximation to JI ==

=== Selected just intervals by error ===

==== Selected 13-limit intervals ====

==== Selected 11-limit intervals ====

[[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]]

=== Interval mappings ===

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== Chords ==

14edo closely approximates the 5:7:9:11:21 chord, mapped to 0–7–12–16–29 steps, and its utonal counterpart, 1/(21:11:9:7:5), mapped to 0–13–17–22–29 steps. One possible approach to 14edo harmony combines these chords, their subsets, inversions, and octave voicings with 14edo’s strongly warped 3-limit framework.

14edo closely approximates the 5:7:9:11:21 chord, mapped to 0–7–12–16–29 steps, and its utonal counterpart, 1/(21:11:9:7:5), mapped to 0–13–17–22–29 steps, as well as the 5:9:11:21:27 chord, mapped to 0–12–16–29–34 steps, and its utonal counterpart, 1/(27:21:11:9:5), mapped to 0–5–18–22–34 steps. One possible approach to 14edo harmony combines these chords, their subsets, inversions, and octave voicings with 14edo’s strongly warped 3-limit framework.

== Diagrams ==

@@ Line 17: / Line 17: @@
 et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.
-edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].
+edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]] or 18:22:27.
 === Prime harmonics ===
@@ Line 257: / Line 257: @@
 == Approximation to JI ==
 === Selected just intervals by error ===
-==== Selected 13-limit intervals ====
+==== Selected 11-limit intervals ====
 [[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]]
 === Interval mappings ===
@@ Line 447: / Line 447: @@
 == Chords ==
-edo closely approximates the 5:7:9:11:21 chord, mapped to 0–7–12–16–29 steps, and its utonal counterpart, 1/(21:11:9:7:5), mapped to 0–13–17–22–29 steps. One possible approach to 14edo harmony combines these chords, their subsets, inversions, and octave voicings with 14edo’s strongly warped 3-limit framework.
+edo closely approximates the 5:7:9:11:21 chord, mapped to 0–7–12–16–29 steps, and its utonal counterpart, 1/(21:11:9:7:5), mapped to 0–13–17–22–29 steps, as well as the 5:9:11:21:27 chord, mapped to 0–12–16–29–34 steps, and its utonal counterpart, 1/(27:21:11:9:5), mapped to 0–5–18–22–34 steps. One possible approach to 14edo harmony combines these chords, their subsets, inversions, and octave voicings with 14edo’s strongly warped 3-limit framework.
 == Diagrams ==

14edo: Difference between revisions

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